MathLinkExtras is Deprecated and all functionality has moved into MathLink v0.5.0

MathLinkExtras

The package adds extra functionality on top of the MathLink package, allowing Julia to talk to Mathematica. For jupyter notebooks, the text/latex MIME-type is implemented.

Usage MathLink

MathLinkExtras is desiged to implement the basic algebraic operation that one expects to excist such as +,-,*,/ and ^.

Just like the MathLink package, the main interface consists of the W"" string macro for specifying symbols.

julia> using MathLink

julia> W"Sin"
W"Sin"

julia> sin1 = W"Sin"(1.0)
W"Sin"(1.0)

julia> sinx = W"Sin"(W"x")
W"Sin"(W"x")

To parse an expression in the Wolfram Language, you can use the W cmd macro (note the backticks):

julia> W`Sin[1]`
W"Sin"(1)

weval evaluates an expression:

julia> weval(sin1)
0.8414709848078965

julia> weval(sinx)
W"Sin"(W"x")

julia> weval(W"Integrate"(sinx, (W"x", 0, 1)))
W"Plus"(1, W"Times"(-1, W"Cos"(1)))

Usage MathLinkExtras

By default MathLinkExtras only overloads the +, -, *, / operations

julia> using MathLink

julia> using MathLinkExtras

julia> W"a"+W"b"
W"Plus"(W"a",W"b")

julia> W"a"+W"a"
W"Plus"(W"a",W"a")

julia> W"a"-W"a"
W"Plus"(W"a",W"Minus"(W"a"))

But one can toggle automatic use of weval on and of using set_GreedyEval(x::Bool)

julia>set_GreedyEval(true)
julia> W"a"+W"b"
W"Plus"(W"a",W"b")

julia> W"a"+W"a"
W"Times"(2,W"a")

julia> W"a"-W"a"
0

Fractions and Complex numbers

The package also contains extentions to handle fractions

julia> weval(1//2)
W"Rational"(1, 2)

julia> (4//5)*W"a"
W"Times"(W"Rational"(4, 5), W"a")

julia> W"a"/(4//5)
W"Times"(W"Rational"(5, 4), W"a")

and complex numbers

julia> im*W"a"
W"Times"(W"Complex"(0, 1), W"a")

julia> im*(im*W"c")
W"Times"(-1, W"c")

W2Tex - Latex conversion

julia> W2Tex(W`(a+b)^(b+x)`)
"(a+b)^{b+x}"

julia> W2Tex(W`a`)
"a"

julia> W2Tex(W`ab`)
"\\text{ab}"

julia> W2Tex(W`ab*cd`)
"\\text{ab} \\text{cd}"

julia> W2Tex(weval(fill(W"a",2,3)))
"\\left(\n\\begin{array}{ccc}\n a & a & a \\\\\n a & a & a \\\\\n\\end{array}\n\\right)"

W2Mstr - Mathematica conversion

Sometimes one wants to be able to read the Julia MathLink expressions back into Mathematica. For that purpose, W2Mstr is also supplied. This implementation is currently quite defensive with parentheses, which gives a more verbose output than necessary. Here are a few examples

julia> W2Mstr(W`x`)
"x"

julia> W2Mstr(W"Sin"(W"x"))
"Sin[x]"

julia> W2Mstr(weval(W`a + c + v`))
"(a + c + v)"

julia> W2Mstr(weval(W`a^(b+c)`))
"(a^(b + c))"

julia> W2Mstr(weval(W`e+a^(b+c)`))
"((a^(b + c)) + e)"

julia> W2Mstr(W"a"+W"c"+W"v"+W"Sin"(2 +W"x" + W"Cos"(W"q")))
"(a + c + v + Sin[(2 + x + Cos[q])])"

julia> W2Mstr(im*2)
"(2*I)"

julia> W2Mstr(weval(W"Complex"(W"c",W"b")))
"(c+b*I)"

julia> W2Mstr(W"c"+im*W"b")
"(((1*I)*b) + c)"

julia> W2Mstr(W`b/(c^(a+c))`)
"(b*((c^(a + c))^-1))"